Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-7x+2y &= 4 \\ 4x+4y &= 8\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $1$ $\begin{align*}14x-4y &= -8\\ 4x+4y &= 8\end{align*}$ Add the top and bottom equations. $18x = 0$ Divide both sides by $18$ and reduce as necessary. $x = 0$ Substitute $0$ for $x$ in the top equation. $-7( 0)+2y = 4$ $2y = 4$ $2y = 4$ $y = 2$ The solution is $\enspace x = 0, \enspace y = 2$.